Expression, equation, identity or formula?

Learning Objective:

• we are learning to distinguish between various bits of algebra and arithmetical statements.

Investing:

• This is useful because we need to learn the language of algebra, so in the same way that it is useful to know a little bit about grammar and the names for bits of speech and text in other languages, we need to have the same handle on the language of algebra
• Algebra is used far more in real life than you might think, although sometimes its uses are not obvious. Here are some links to people using quite sophisticated algebra to solve problems using algebraic computing.
  • example computable documents from Wolfram CDF (you may need to download and install the free Wolfram CDF player)
  • using dynamic algebra to improve toothbrush design
  • using mathematical modelling to increase air traffic
  • communicating the complexity of the real-world with dynamic infographics
  • making a modular Olympic velodrome a 'snap'
• This skill leads to simplifying algebra and manipulating algebra
• This could help you if you want to work in a huge range of scientific, financial and engineering jobs.

Preparing:

• Are we ready? Have you met the idea of using a letter to stand for a number either as an unknown to be found or a variable that can change?
• Can you give examples of each?
• Before you start you need to know some of the basic conventions of algebraic notation such as writing 3x to mean 3 multiplied by the value of x.
• You will have a deeper understanding if you also know some subtleties such as why it is impossible to divide by zero and that certain equations may have multiple solutions.

Discovering:

• Can you figure it out yourself from these examples?
• Try to predict the next one aloud or on a mini-whiteboard.
• Investigate...

Modeling:

• Here are some examples of people getting it right:
• Here are some examples of people getting it wrong in typical ways:
• Here are some more examples. Did they get it right or wrong? Explain how you know!

Discussing:

• A useful flash game from MathsFlash:

• What would this one be? Tell your learning partner. Convince them you're right.
• Explain how you know.
• How would you explain this to someone who was new to it?

Explaining:

• Math4teaching: fun with definitions in algebra
• Another approach might be...
• A useful shortcut is to...
• This works because...
• It doesn't work when...
• An exception is...
• Watch out for...
• A common mistake is...
• You can check your result by...
• We can prove this works by...

Practicing:

• Some straightforward examples.
• Some harder examples.
• Some mixed examples.
• Some non-examples to spot and some mixed questions with redundant, insufficient or contradictory data.
• You can demonstrate fluency by at least...

Sharing:

• A web page or wiki I have created to explain this can be found at...
• A presentation I have created and rehearsed looks like...
• A poster I have drawn or model I have made can be found...

Assessing:

• Check you've mastered this skill by...
• Show you understand by explaining...
• Prove you're an expert in... by...

Developing:

• Next we could learn...
• This leads to...
• Now try...